# Operation Research MCQ for SAIL MT Materials

Q1. When the problem involves the allocation of n different facilities to n different tasks, it is often termed as an ….....................
(a) Transportation problem
(b) Game theory.
(c) Integer programming problem
(d) Assignment problem

Q2. When there is no column and no row without assignment. In such case, the current assignment is…………………..
(a) Maximum
(b) Optimal
(c) Minimum
(d) Zero

Q3.  Not returning to the node already passed through or passing through every node once and only once. Problem of such type are called as ……………….
(a) Assignment problem
(b) Transportation problem
(c) I.P.P
(d) Routing problem

Q4. (i) N = n. then assignment is optimal
(ii) N<n. then assignment is ………………..
(a) less
(b) More
(c) Equal
(d) Not optimal

Q5.An assignment problem can be formulated as a linear programming problem, it is solved by special method know as…………….
(a) Gomary,s method
(b) Hungarian method
(c) Branch and bound method
(d) Queuing model

Q6. Consider the problem of assigning five jobs to five person. The assignment costs are given as follows:-
 Job Persons 1 2 3 4 5 A 8 4 2 6 1 B 0 9 5 5 4 C 3 8 9 2 6 D 4 3 1 0 3 E 9 5 8 9 5
Determine the optimum assignment cost.
(a) 10
(b) 8
(c) 9
(d) 11

Q7. Four jobs are to be done on four different machines. The cost in (rupees) of producing  ith  on the  jth  machines is given below.
 MACHINES JOBS M1 M2 M3 M4 J1 15 11 13 15 J2 17 12 12 13 J3 14 15 10 14 J4 16 13 11 17
Assign the jobs to different machines so a to minimize the total cost.
(a) 50
(b) 52
(c) 54
(d) 49

Q8.As the no. of persons is the same as the number of jobs, ……………is said to be balanced.
(a) Assignment problem
(b) Hungarian method
(c) L.P.P
(d) Transportation problem

Q9. A marketing manager has 5 salesmen and 5 sales districts. Considering the capabilities of the salesman and the nature of districts, the marketing manager estimates that sales per month (in hundred rupees) for each salesmen in each district would be as follows.
 Sales districts Salesman A B C D E 1 32 38 40 28 40 2 40 24 28 21 36 3 41 27 33 30 37 4 22 38 41 36 36 5 29 33 40 35 39
Find the assignment of salesman to districts that will result in maximum sales. So the maximum sales is………………
(a) 20001
(b) 19100
(c) 18200
(d) 20100

Q10………..is a special case of L.P.P where all or some variables are constrained to assume non-negative integer values.
(a) Transportation problem
(b) L.P.P
(c) Gomory’s method
(d) I.P.P

Q11………………problem has lot of applications in business and industry where quite often discrete nature of the variables is involved in many decision making situation.
(a) I.P.P
(b) L.P.P
(c) Assignment problem
(d)Simplex method

Q12.If  all the variables are constrained to take only integral value i.e. k=n, it is  called an ………….. integer programming problem .
(a)  one
(b)  many
(c)   all(pure)
(d)  none

Q13.Only some of the variables are restricted to take integral value and rest (n-k) variables are free to take any non-negative values, then the problem is known as……………… integer programming problem.
(a)  single
(b) mixed
(c)   both (a) and (b)
(d)  none of these

Q14. Find the optimum integer solution to the following all I.P.P.
Maximize            z=X1+2X2
Subject to the constraints
X1 + X2   ≤ 7
2X1          ≤ 11
2X≤ 7
X1, X2   ≥ 0 and are integers
The integer optimum solution to the IPP is…………………..
(a) X1=4, X2=3
And max Z=10
(b) X1=6, X2=2
And max Z=9
(c) X1=3, X2=4
And max Z=11
(e)   None of these.

Q15 Use branch and bound technique to solve the following I.P.P.
Maximize                 Z=7x1+9x2 ------------------------- (1)
Subject to the constraints
-x1 + 3x2≤ 6------------------------- (2)
7x1+ x2 ≤ 35
0≤ x1, x2 ≤ 7----------------------- (3)
X1, x2 are integers --------------------- (4)
Hence the optimum integer solution to the given I.P.P. is
(a)  Zo=55, X1=4, X2=3
(b)  Zo=45, X1= 6, X2=2
(c)   Both (a) and(b)
(d)  None of these

Q16. Use branch and bound techniques to solve the following problems
Max Z=3X1+3X2+13X3
Subject to
-3X1 +6X2+7X3≤8
6X1-3X2+7X3≤ 8
0≤Xj≤5
And Xj are integer j=1, 2, 3
(a)  X1=X2=0, X3=1, Z*=13
(b)  X1=X2=2, X3=0, Z*=14
(c)   X1=1,X2=0, X3=0, Z*=10
(d)  None of these

Q17 ………………… are the two algorithms to determine the optimal solution for an integer programming problem.
(a)  Simplex and branch and bound method
(b)  Branch and bound and simulation method
(c)   Cutting plane algorithm and branch and bound  algorithm
(d)  None of these.

Q18. Cutting plane algorithms is devised by………………
(a)   Land and Doig
(b)  Gomory
(c)   Both (a) and (b)
(d)  None of these

Q19. branch and bound algorithm is developed by………………..
(a)  Land and Doig
(b)  Erlang
(c)   Both (a) and (b)
(d)  None of these

Q20. In the optimum solution if all the variables have ………….. values, the current solution will be desired optimum integer solution.
(a)  Integer
(b)  Positive
(c)   Negative
(d)  None of these.

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